It becomes a trivial exercise to modify designs to ensure the relevant polar regions are covered. It projects the 3D space from an arbitrary viewpoint together with geometry in the 3D space corresponding to things like amplifier stability regions. The 3D Smith chart seeks to let you simultaneously "see" the north, south, east, and west poles so that you can solve certain problems graphically.
There are certain design situations where you need to "see" open and short circuit conditions simultaneously. You can do that, too, with a 2D Smith chart but then you can't "see" short circuits. If you wanted to explore the poles, you could construct a different projection that preserved polar distances but compromised "east" and "west". The choice of the equator in a Mercator projection is arbitrary. Using 2D Smith projections, they are like polar explorers trying to use an equatorial Mercator projection - they can't "see" anything. This is an important region for people like microwave designers and negative amplifier designers. In the 2D Smith projection, the "thing that is being compromised" is the behaviour of certain types of electronic circuits called "active circuits" under condition of open circuit.
The further away you get from the equator, the more that breaks down until, at the poles, there is no correspondence at all.Īn equatorial Mercator projection is great for exploring the equatorial region. In an equatorial Mercator projection, the line around the equator yields a proportional representation of distance. In a projection you always have to compromise something. In visualising the surface of the spherical earth on a piece of paper, we use a projection, for example the Mercator. It is analogous to representing the 3D surface of the earth on a 2D surface. The 2D chart is trying to represent what is, in fact a 3D phenomenon. Thanks, Argyle! Any chance you could take a shot at explaining the problem that this article is trying to solve? In the days before widespread use of circuit design software, these kinds of diagrams were critical to properly designing things like radars, radio towers and receivers, televisions, and basically all forms of wireless communication and transmission. The math gets complicated fast and is difficult to visualize in your head.Ī Smith chart allows an engineer to visualize a circuit, or partial circuit, to determine if it does what they want, or what changes to the circuit are necessary to make it do what they want. The physical properties of the transmission medium affect properties like capacitance, impedance, and inductance. RF at these wavelengths interacts with the physicality of whatever it's transmitted through, air, waveguide, cables, etc. Physicality of the environment has a huge effect on the RF waves. The RF waves used in the microwave are so long, that can't fit through the small holes. For example, there are small holes in the 'window' of your microwave oven. If you can imagine an RF wave like a up and down sine curve traveling through space, the distance between 'humps' would be something you could measure with a ruler. Radio Frequencies (RF) at the wavelength that you would look at are at the human scale, millimeter, meters, etc. Even built a program that graphed Smith charts in the 80s. Hrrm, I actually studied a lot of electromagnetics and microwave engineering in college.
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